A uniform disc of mass m and radius r is pivoted at point P and is free to rotate in - Physics - System Of Particles And Rotational Motion

Question

A uniform disc of mass m and radius r is pivoted at point P and is
free to rotate in vertical plane The centre C of disc is initially
in horizontal position with P If it is released from this position
, then its angular acceleration when the line PC is inclined to the
horizontal at angle Q ?

Peter Fernandes · Accepted Answer

Moment of inertia of a disc about its
centre is12mr2
When the disc makes an angle Q with the horizontal
<img alt="" height="99" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/Disc%20png"
width="71">
Consider the distance between P and C to be x
Then the moment of inertia about P is
I=I0+mx2I=12mr2+mx2
Hence
mgcosQx=Iαα=2mgxcosQmr2+2x2α=2gxcosQr2+2x2

A uniform disc of mass m and radius r is pivoted at point P and is free to rotate in vertical plane . The centre C of disc is initially in horizontal position with P .If it is released from this position , then its angular acceleration when the line PC is inclined to the horizontal at angle Q ?